directional derivative,

A problem asks me to show that no real-valued function f has a
positive directional derivative at a fixed point c for every possible
direction u.

But wouldn't a paraboloid work? Fix c corresponding to the vertex.
Then for any direction u, the slope will always be positive
(increasing).

To be clear, the exact problem is worded: Prove that there is no real-
valued function f such that f'(c;u) > 0 for a fixed point c in R^n and
every nonzero vector u in R^n.

.